Question

Please help me solve this problem.

Image text transcribed for accessibility:For a linear second order differential equation, the text explains that there are only three possible solutions: two distinct real roots (over damped), two equal real roots (critically damped), and two complex roots (under damped). When the two roots are equal, prove that for f(t) = a2 dx2n/ dt2+a1dxn/dt+a0xn where f(t) =0 xn = e s1t (A1t+A2) Since it is already known that A2es1t is a solution, you only have to prove that A1tes1t is a solution.